About this Journal Submit a Manuscript Table of Contents
Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 796842, 8 pages
http://dx.doi.org/10.1155/2013/796842
Research Article

The Analysis of Braess’ Paradox and Robustness Based on Dynamic Traffic Assignment Models

1School of Architecture and Urban Planning, Shandong Jianzhu University, Jinan 250101, China
2School of Mathematics and Statistics, Anyang Normal University, Anyang 455000, China
3Public Security Department, Shandong Police College, Jinan 250014, China

Received 25 July 2013; Accepted 24 October 2013

Academic Editor: Wuhong Wang

Copyright © 2013 Bai-Bai Fu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. R. Birge and J. K. Ho, “Optimal flows in stochastic dynamic networks with congestion,” Operations Research, vol. 41, no. 1, pp. 203–216, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. B. N. Janson, “Dynamic traffic assignment for urban road networks,” Transportation Research B, vol. 25, no. 2-3, pp. 143–161, 1991. View at Scopus
  3. B.-W. Wie, T. L. Friesz, and R. L. Tobin, “Dynamic user optimal traffic assignment on congested multidestination networks,” Transportation Research B, vol. 24, no. 6, pp. 431–442, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  4. B. Ran, D. E. Boyce, and L. J. LeBlanc, “New class of instantaneous dynamic user-optimal traffic assignment models,” Operations Research, vol. 41, no. 1, pp. 192–202, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  5. H.-K. Chen and C.-F. Hsueh, “A model and an algorithm for the dynamic user-optimal route choice problem,” Transportation Research B, vol. 32, no. 3, pp. 219–234, 1998. View at Publisher · View at Google Scholar · View at Scopus
  6. R. Jayakrishnan, W. K. Tsai, and A. Chen, “A dynamic traffic assignment model with traffic-flow relationships,” Transportation Research C, vol. 3, no. 1, pp. 51–72, 1995. View at Publisher · View at Google Scholar · View at Scopus
  7. X. J. Nie, The study of dynamic user-equilibrium traffic assignment [Ph.D. thesis], University of California, Davis, Calif, USA, 2003.
  8. S. C. Dafermos and F. T. Sparrow, “The traffic assignment problem for a general network,” Journal of Research of the National Bureau of Standards, vol. 73, pp. 91–118, 1969. View at Zentralblatt MATH · View at MathSciNet
  9. M. J. Smith, “The existence, uniqueness and stability of traffic equilibria,” Transportation Research B, vol. 13, no. 4, pp. 295–304, 1979. View at Publisher · View at Google Scholar · View at MathSciNet
  10. M. Ng and S. T. Waller, “A dynamic route choice model considering uncertain capacities,” Computer-Aided Civil and Infrastructure Engineering, vol. 27, no. 4, pp. 231–243, 2012. View at Publisher · View at Google Scholar · View at Scopus
  11. Q. Meng and H. L. Khoo, “A computational model for the probit-based dynamic stochastic user optimal traffic assignment problem,” Journal of Advanced Transportation, vol. 46, no. 1, pp. 80–94, 2012. View at Publisher · View at Google Scholar · View at Scopus
  12. S. Dafermos, “Traffic equilibrium and variational inequalities,” Transportation Science, vol. 14, no. 1, pp. 42–54, 1980. View at Publisher · View at Google Scholar · View at MathSciNet
  13. D. Braess, “Über ein paradoxon aus der verkehrsplanung,” Unternehmensforschung, vol. 12, pp. 258–268, 1968. View at Zentralblatt MATH · View at MathSciNet
  14. S. Dafermos and A. Nagurney, “On some traffic equilibrium theory paradoxes,” Transportation Research B, vol. 18, no. 2, pp. 101–110, 1984. View at Publisher · View at Google Scholar · View at MathSciNet
  15. T. Akamatsu and B. Heydecker, “Detecting dynamic traffic assignment capacity paradoxes in saturated networks,” Transportation Science, vol. 37, no. 2, pp. 123–138, 2003. View at Publisher · View at Google Scholar · View at Scopus
  16. T. Roughgarden, Selfish Routing and the Price of Anarchy, MIT Press, 2005.
  17. X. Zhang and H. M. Zhang, “Simultaneous departure time/route choices in queueing networks and a novel paradox,” Networks and Spatial Economics, vol. 10, no. 1, pp. 93–112, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  18. E. I. Pas and S. L. Principio, “Braess' paradox: some new insights,” Transportation Research B, vol. 31, no. 3, pp. 265–276, 1997. View at Publisher · View at Google Scholar · View at Scopus
  19. R. Arnott, A. de Palma, and R. Lindsey, “Properties of dynamic traffic equilibrium involving bottlenecks, including a paradox and metering,” Transportation Science, vol. 27, no. 2, pp. 148–160, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  20. A. Hallefjord, K. Jörnsten, and S. Storøy, “Traffic equilibrium paradoxes when travel demand is elastic,” Asia-Pacific Journal of Operational Research, vol. 11, no. 1, pp. 41–50, 1994. View at Zentralblatt MATH · View at MathSciNet
  21. X. Zhang, W. H. K. Lam, and H.-J. Huang, “Braess's paradoxes in dynamic traffic assignment with simultaneous departure time and route choices,” Transportmetrica, vol. 4, no. 3, pp. 209–225, 2008. View at Publisher · View at Google Scholar · View at Scopus
  22. J. N. Prashker and S. Bekhor, “Some observations on stochastic user equilibrium and system optimum of traffic assignment,” Transportation Research B, vol. 34, no. 4, pp. 277–291, 2000. View at Publisher · View at Google Scholar · View at Scopus
  23. A. Nagurney and Q. Qiang, “A relative total cost index for the evaluation of transportation network robustness in the presence of degradable links and alternative travel behavior,” International Transactions in Operational Research, vol. 16, no. 1, pp. 49–67, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. A. Nagurney, Q. Qiang, and L. S. Nagurney, “Environmental impact assessment of transportation networks with degradable links in an era of climate change,” International Journal of Sustainable Transportation, vol. 4, no. 3, pp. 154–171, 2010. View at Publisher · View at Google Scholar · View at Scopus
  25. A. Nagurney and Q. Qiang, “A network efficiency measure for congested networks,” Europhysics Letters, vol. 79, no. 3, Article ID 38005, 5 pages, 2007. View at Publisher · View at Google Scholar · View at Scopus